{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.cluster import DBSCAN\n",
    "from sklearn.metrics import homogeneity_score\n",
    "\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram\n",
    "\n",
    "np.set_printoptions(suppress=True, precision=5)\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples = 150, n_features=2, \n",
    "                  centers=3, cluster_std=0.5, shuffle=True, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X2')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c = \"steelblue\", marker = \"o\", s = 50)\n",
    "plt.xlabel(\"X1\")\n",
    "plt.ylabel(\"X2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters=3, init=\"random\", n_init = 10, \n",
    "            max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def show_cluster(X, y, estimator = None, ignore_noise = True):\n",
    "    levels = set(y)\n",
    "    \n",
    "    if ignore_noise and -1 in levels:\n",
    "        levels.remove(-1)\n",
    "    \n",
    "    colors = sns.color_palette(\"husl\", len(levels))\n",
    "    centroids = None \n",
    "    if estimator is not None and hasattr(estimator, \"cluster_centers_\"):\n",
    "        centroids = estimator.cluster_centers_  \n",
    "\n",
    "    for k in levels:\n",
    "        data = X[y == k, :]\n",
    "        plt.scatter(data[:, 0], data[:, 1], color = colors[k], s = 50, label = \"Cluster %s\" % k)\n",
    "\n",
    "    if not centroids is None:\n",
    "        plt.scatter(centroids[:, 0], centroids[:, 1], color = \"black\", marker = \"*\", s = 150)\n",
    "\n",
    "    plt.xlabel(\"X1\")\n",
    "    plt.ylabel(\"X2\")\n",
    "    plt.legend(loc = \"lower left\")\n",
    "    \n",
    "show_cluster(X, y_km, km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.93297,  4.35421],\n",
       "       [ 2.06522,  0.96137],\n",
       "       [-1.59473,  2.92237]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "km.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distortion (Within Cluster SSE): 72.48\n"
     ]
    }
   ],
   "source": [
    "#Sum of distances of samples to their closest cluster center.\n",
    "print(\"Distortion (Within Cluster SSE): %.2f\" % km.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Sum of distances of samples to their closest cluster center.\n",
    "homogeneity_score(y, y_km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Homogeneity score:  0.6812190697089529 Inertia:  262.72046565264066\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated clusters')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = make_blobs(n_samples = 150, n_features=2, centers=3, \n",
    "                  cluster_std=1.0, shuffle=True, random_state=0)\n",
    "km = KMeans(n_clusters=3, init=\"random\", n_init = 10, \n",
    "            max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "print(\"Homogeneity score: \", homogeneity_score(y, y_km), \"Inertia: \", km.inertia_)\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y, km)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_km, km)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find optimal number of clusters using elbow method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def find_elbow(X, n = 10):\n",
    "    distortions = []\n",
    "    for i in range(1, n):\n",
    "        km = KMeans(n_clusters=i, max_iter=300, n_init=10, random_state=0, init=\"k-means++\")\n",
    "        km.fit(X)\n",
    "        distortions.append(km.inertia_)\n",
    "    plt.plot(range(1, n), distortions)\n",
    "    plt.xlabel(\"Number of clusters (K)\")\n",
    "    plt.ylabel(\"Distortion\")\n",
    "\n",
    "find_elbow(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find number of clusters from Dendogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 10))\n",
    "row_clusters = linkage(X, method=\"complete\", metric=\"euclidean\")\n",
    "f = dendrogram(row_clusters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Half Moon Dataset and DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_moons(n_samples=200, noise=0.09, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X2')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c = \"steelblue\", marker = \"o\", s = 50)\n",
    "plt.xlabel(\"X1\")\n",
    "plt.ylabel(\"X2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated clusters')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(n_clusters=2, init=\"random\", n_init = 10, max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "#show_cluster(km, X, y_km)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_km, km)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1810982320182603"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "homogeneity_score(y, y_km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated clusters')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbscan = DBSCAN(eps=0.2, min_samples=10, metric=\"euclidean\")\n",
    "y_db = dbscan.fit_predict(X)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y, dbscan)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_db, dbscan)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of clusters:  7\n"
     ]
    }
   ],
   "source": [
    "labels = set(y_db)\n",
    "if -1 in labels: #Noise\n",
    "    labels.remove(-1)\n",
    "print(\"No of clusters: \", len(labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9395815602003369"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "homogeneity_score(y, y_db)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying clustering to grouplens movies dataset based on genre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toy Story (1995)</td>\n",
       "      <td>Adventure|Animation|Children|Comedy|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Jumanji (1995)</td>\n",
       "      <td>Adventure|Children|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Grumpier Old Men (1995)</td>\n",
       "      <td>Comedy|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Waiting to Exhale (1995)</td>\n",
       "      <td>Comedy|Drama|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Father of the Bride Part II (1995)</td>\n",
       "      <td>Comedy</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                      title  \\\n",
       "movieId                                       \n",
       "1                          Toy Story (1995)   \n",
       "2                            Jumanji (1995)   \n",
       "3                   Grumpier Old Men (1995)   \n",
       "4                  Waiting to Exhale (1995)   \n",
       "5        Father of the Bride Part II (1995)   \n",
       "\n",
       "                                              genres  \n",
       "movieId                                               \n",
       "1        Adventure|Animation|Children|Comedy|Fantasy  \n",
       "2                         Adventure|Children|Fantasy  \n",
       "3                                     Comedy|Romance  \n",
       "4                               Comedy|Drama|Romance  \n",
       "5                                             Comedy  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies = pd.read_csv(\"/data/movielens/movies.csv\", index_col=\"movieId\")\n",
    "movies.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2202</th>\n",
       "      <td>Lifeboat (1944)</td>\n",
       "      <td>Drama|War</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>Michael Collins (1996)</td>\n",
       "      <td>Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4863</th>\n",
       "      <td>Female Trouble (1975)</td>\n",
       "      <td>Comedy|Crime</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>647</th>\n",
       "      <td>Courage Under Fire (1996)</td>\n",
       "      <td>Action|Crime|Drama|War</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85788</th>\n",
       "      <td>Insidious (2010)</td>\n",
       "      <td>Fantasy|Horror|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>963</th>\n",
       "      <td>Inspector General, The (1949)</td>\n",
       "      <td>Musical</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4570</th>\n",
       "      <td>Big Picture, The (1989)</td>\n",
       "      <td>Comedy|Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55999</th>\n",
       "      <td>Mr. Magorium's Wonder Emporium (2007)</td>\n",
       "      <td>Children|Comedy|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>640</th>\n",
       "      <td>Diabolique (1996)</td>\n",
       "      <td>Drama|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960</th>\n",
       "      <td>Last Emperor, The (1987)</td>\n",
       "      <td>Drama</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         title                   genres\n",
       "movieId                                                                \n",
       "2202                           Lifeboat (1944)                Drama|War\n",
       "991                     Michael Collins (1996)                    Drama\n",
       "4863                     Female Trouble (1975)             Comedy|Crime\n",
       "647                  Courage Under Fire (1996)   Action|Crime|Drama|War\n",
       "85788                         Insidious (2010)  Fantasy|Horror|Thriller\n",
       "963              Inspector General, The (1949)                  Musical\n",
       "4570                   Big Picture, The (1989)             Comedy|Drama\n",
       "55999    Mr. Magorium's Wonder Emporium (2007)  Children|Comedy|Fantasy\n",
       "640                          Diabolique (1996)           Drama|Thriller\n",
       "1960                  Last Emperor, The (1987)                    Drama"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3979</th>\n",
       "      <td>Little Nicky (2000)</td>\n",
       "      <td>Comedy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5223</th>\n",
       "      <td>Pauline &amp; Paulette (Pauline en Paulette) (2001)</td>\n",
       "      <td>Comedy|Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51094</th>\n",
       "      <td>Gray Matters (2006)</td>\n",
       "      <td>Comedy|Drama|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2828</th>\n",
       "      <td>Dudley Do-Right (1999)</td>\n",
       "      <td>Children|Comedy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80083</th>\n",
       "      <td>Dragon Ball Z: Dead Zone (Doragon bôru Z 1: Or...</td>\n",
       "      <td>Action|Adventure|Animation|Fantasy|Sci-Fi</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113640</th>\n",
       "      <td>Canal, The (2014)</td>\n",
       "      <td>Horror|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6299</th>\n",
       "      <td>Winged Migration (Peuple migrateur, Le) (2001)</td>\n",
       "      <td>Documentary</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1192</th>\n",
       "      <td>Paris Is Burning (1990)</td>\n",
       "      <td>Documentary</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68901</th>\n",
       "      <td>Chop Shop (2007)</td>\n",
       "      <td>Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3032</th>\n",
       "      <td>Omega Man, The (1971)</td>\n",
       "      <td>Action|Drama|Sci-Fi|Thriller</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     title  \\\n",
       "movieId                                                      \n",
       "3979                                   Little Nicky (2000)   \n",
       "5223       Pauline & Paulette (Pauline en Paulette) (2001)   \n",
       "51094                                  Gray Matters (2006)   \n",
       "2828                                Dudley Do-Right (1999)   \n",
       "80083    Dragon Ball Z: Dead Zone (Doragon bôru Z 1: Or...   \n",
       "113640                                   Canal, The (2014)   \n",
       "6299        Winged Migration (Peuple migrateur, Le) (2001)   \n",
       "1192                               Paris Is Burning (1990)   \n",
       "68901                                     Chop Shop (2007)   \n",
       "3032                                 Omega Man, The (1971)   \n",
       "\n",
       "                                            genres  \n",
       "movieId                                             \n",
       "3979                                        Comedy  \n",
       "5223                                  Comedy|Drama  \n",
       "51094                         Comedy|Drama|Romance  \n",
       "2828                               Children|Comedy  \n",
       "80083    Action|Adventure|Animation|Fantasy|Sci-Fi  \n",
       "113640                             Horror|Thriller  \n",
       "6299                                   Documentary  \n",
       "1192                                   Documentary  \n",
       "68901                                        Drama  \n",
       "3032                  Action|Drama|Sci-Fi|Thriller  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies = movies[~movies[\"genres\"].str.contains(\"\\(no genres listed\\)\")]\n",
    "movies.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Action', 'Adventure', 'Animation', 'Children', 'Comedy', 'Crime', 'Documentary', 'Drama', 'Fantasy', 'Film-Noir', 'Horror', 'IMAX', 'Musical', 'Mystery', 'Romance', 'Sci-Fi', 'Thriller', 'War', 'Western'] 19\n"
     ]
    }
   ],
   "source": [
    "genres = set()\n",
    "movies[\"genres\"].apply(lambda g: genres.update(g.split(r\"|\")))\n",
    "genres = list(genres)\n",
    "genres.sort()\n",
    "print(genres, len(genres))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "movieId\n",
       "1     [0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, ...\n",
       "2     [0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, ...\n",
       "3     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "4     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, ...\n",
       "5     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "6     [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, ...\n",
       "7     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "8     [0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "9     [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "10    [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "Name: genres, dtype: object"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def to_vector(g):\n",
    "    indices = np.array([genres.index(v) for v in g.split(r\"|\")])\n",
    "    l = np.zeros(len(genres))\n",
    "    l[indices] = 1\n",
    "    return l\n",
    "\n",
    "genres_idx = movies[\"genres\"].apply(to_vector)\n",
    "genres_idx.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape:  (9107, 19)\n"
     ]
    }
   ],
   "source": [
    "X = np.array(genres_idx.tolist())\n",
    "print(\"X.shape: \", X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 10))\n",
    "row_clusters = linkage(X_std, method=\"complete\", metric=\"euclidean\")\n",
    "f = dendrogram(row_clusters, p = 5, truncate_mode=\"level\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the clusters lets apply PCA with 2 components. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import KernelPCA, PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Number of PCA components')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(random_state=0)\n",
    "X_pca = pca.fit_transform(X_std)\n",
    "\n",
    "ratios = pca.explained_variance_ratio_\n",
    "plt.bar(range(len(ratios)), ratios)\n",
    "plt.step(range(len(ratios)), np.cumsum(ratios), \n",
    "         label = \"Cumsum of Explained variance ratio\")\n",
    "plt.title(\"Explained variance\")\n",
    "plt.ylabel(\"Explained Variance Ratio\")\n",
    "plt.xlabel(\"Number of PCA components\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With 2 principle components havelow explained variance coverage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PCA2')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(random_state=0, n_components=2)\n",
    "X_pca = pca.fit_transform(X_std)\n",
    "\n",
    "plt.figure(figsize = (15, 8))\n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1])\n",
    "plt.xlabel(\"PCA1\")\n",
    "plt.ylabel(\"PCA2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is not visual indication of clusters from 2 PCA components which is consistent with the finding that explained variance with 2 components is only 2%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "find_elbow(X_std, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn = KMeans(n_clusters=8, max_iter=300, random_state=0)\n",
    "y_pred = knn.fit_predict(X_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each observations, compute distance to the nearest cluster centroid. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>81132</th>\n",
       "      <td>Rubber (2010)</td>\n",
       "      <td>Action|Adventure|Comedy|Crime|Drama|Film-Noir|...</td>\n",
       "      <td>10.008449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81847</th>\n",
       "      <td>Tangled (2010)</td>\n",
       "      <td>Animation|Children|Comedy|Fantasy|Musical|Roma...</td>\n",
       "      <td>8.401892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83613</th>\n",
       "      <td>Cowboys &amp; Aliens (2011)</td>\n",
       "      <td>Action|Sci-Fi|Thriller|Western|IMAX</td>\n",
       "      <td>8.313656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>595</th>\n",
       "      <td>Beauty and the Beast (1991)</td>\n",
       "      <td>Animation|Children|Fantasy|Musical|Romance|IMAX</td>\n",
       "      <td>8.223587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2142</th>\n",
       "      <td>American Tail: Fievel Goes West, An (1991)</td>\n",
       "      <td>Adventure|Animation|Children|Musical|Western</td>\n",
       "      <td>8.047143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103384</th>\n",
       "      <td>Lone Ranger, The (2013)</td>\n",
       "      <td>Action|Adventure|Western|IMAX</td>\n",
       "      <td>7.930896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7374</th>\n",
       "      <td>Home on the Range (2004)</td>\n",
       "      <td>Animation|Children|Comedy|Musical|Western</td>\n",
       "      <td>7.822317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>364</th>\n",
       "      <td>Lion King, The (1994)</td>\n",
       "      <td>Adventure|Animation|Children|Drama|Musical|IMAX</td>\n",
       "      <td>7.558606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3159</th>\n",
       "      <td>Fantasia 2000 (1999)</td>\n",
       "      <td>Animation|Children|Musical|IMAX</td>\n",
       "      <td>7.416244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26701</th>\n",
       "      <td>Patlabor: The Movie (Kidô keisatsu patorebâ: T...</td>\n",
       "      <td>Action|Animation|Crime|Drama|Film-Noir|Mystery...</td>\n",
       "      <td>7.396372</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     title  \\\n",
       "movieId                                                      \n",
       "81132                                        Rubber (2010)   \n",
       "81847                                       Tangled (2010)   \n",
       "83613                              Cowboys & Aliens (2011)   \n",
       "595                            Beauty and the Beast (1991)   \n",
       "2142            American Tail: Fievel Goes West, An (1991)   \n",
       "103384                             Lone Ranger, The (2013)   \n",
       "7374                              Home on the Range (2004)   \n",
       "364                                  Lion King, The (1994)   \n",
       "3159                                  Fantasia 2000 (1999)   \n",
       "26701    Patlabor: The Movie (Kidô keisatsu patorebâ: T...   \n",
       "\n",
       "                                                    genres   distance  \n",
       "movieId                                                                \n",
       "81132    Action|Adventure|Comedy|Crime|Drama|Film-Noir|...  10.008449  \n",
       "81847    Animation|Children|Comedy|Fantasy|Musical|Roma...   8.401892  \n",
       "83613                  Action|Sci-Fi|Thriller|Western|IMAX   8.313656  \n",
       "595        Animation|Children|Fantasy|Musical|Romance|IMAX   8.223587  \n",
       "2142          Adventure|Animation|Children|Musical|Western   8.047143  \n",
       "103384                       Action|Adventure|Western|IMAX   7.930896  \n",
       "7374             Animation|Children|Comedy|Musical|Western   7.822317  \n",
       "364        Adventure|Animation|Children|Drama|Musical|IMAX   7.558606  \n",
       "3159                       Animation|Children|Musical|IMAX   7.416244  \n",
       "26701    Action|Animation|Crime|Drama|Film-Noir|Mystery...   7.396372  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def distance(p1, p2):\n",
    "    p1, p2 = p1.flatten(), p2.flatten()\n",
    "    return np.sqrt(np.sum((p1 - p2) ** 2))\n",
    "\n",
    "distances = []\n",
    "for i in range(X_std.shape[0]):\n",
    "    p1 = X_std[i, :]\n",
    "    cluster = knn.labels_[i]\n",
    "    center = knn.cluster_centers_[cluster]\n",
    "    distances.append(distance(p1, center))\n",
    "\n",
    "movies[\"distance\"] = np.array(distances)\n",
    "movies.sort_values(\"distance\", ascending=False)[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2367</th>\n",
       "      <td>King Kong (1976)</td>\n",
       "      <td>Adventure|Fantasy|Romance|Sci-Fi|Thriller</td>\n",
       "      <td>6.439895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156607</th>\n",
       "      <td>The Huntsman Winter's War (2016)</td>\n",
       "      <td>Action|Adventure|Drama|Fantasy</td>\n",
       "      <td>5.160459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51698</th>\n",
       "      <td>Last Mimzy, The (2007)</td>\n",
       "      <td>Adventure|Children|Sci-Fi</td>\n",
       "      <td>5.026697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104419</th>\n",
       "      <td>Justice League: Crisis on Two Earths (2010)</td>\n",
       "      <td>Action|Animation|Sci-Fi</td>\n",
       "      <td>5.577885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Tom and Huck (1995)</td>\n",
       "      <td>Adventure|Children</td>\n",
       "      <td>4.047729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30810</th>\n",
       "      <td>Life Aquatic with Steve Zissou, The (2004)</td>\n",
       "      <td>Adventure|Comedy|Fantasy</td>\n",
       "      <td>4.594276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99764</th>\n",
       "      <td>It's Such a Beautiful Day (2012)</td>\n",
       "      <td>Animation|Comedy|Drama|Fantasy|Sci-Fi</td>\n",
       "      <td>5.681293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3287</th>\n",
       "      <td>Tigger Movie, The (2000)</td>\n",
       "      <td>Animation|Children</td>\n",
       "      <td>3.966153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95311</th>\n",
       "      <td>Presto (2008)</td>\n",
       "      <td>Animation|Children|Comedy|Fantasy</td>\n",
       "      <td>4.163322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>919</th>\n",
       "      <td>Wizard of Oz, The (1939)</td>\n",
       "      <td>Adventure|Children|Fantasy|Musical</td>\n",
       "      <td>5.874266</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                               title  \\\n",
       "movieId                                                \n",
       "2367                                King Kong (1976)   \n",
       "156607              The Huntsman Winter's War (2016)   \n",
       "51698                         Last Mimzy, The (2007)   \n",
       "104419   Justice League: Crisis on Two Earths (2010)   \n",
       "8                                Tom and Huck (1995)   \n",
       "30810     Life Aquatic with Steve Zissou, The (2004)   \n",
       "99764               It's Such a Beautiful Day (2012)   \n",
       "3287                        Tigger Movie, The (2000)   \n",
       "95311                                  Presto (2008)   \n",
       "919                         Wizard of Oz, The (1939)   \n",
       "\n",
       "                                            genres  distance  \n",
       "movieId                                                       \n",
       "2367     Adventure|Fantasy|Romance|Sci-Fi|Thriller  6.439895  \n",
       "156607              Action|Adventure|Drama|Fantasy  5.160459  \n",
       "51698                    Adventure|Children|Sci-Fi  5.026697  \n",
       "104419                     Action|Animation|Sci-Fi  5.577885  \n",
       "8                               Adventure|Children  4.047729  \n",
       "30810                     Adventure|Comedy|Fantasy  4.594276  \n",
       "99764        Animation|Comedy|Drama|Fantasy|Sci-Fi  5.681293  \n",
       "3287                            Animation|Children  3.966153  \n",
       "95311            Animation|Children|Comedy|Fantasy  4.163322  \n",
       "919             Adventure|Children|Fantasy|Musical  5.874266  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies[y_pred == 3].sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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